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An embedding of the
Morse boundary in the Martin boundary
Matthew Cordes, Matthieu Dussaule and Ilya Gekhtman |
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Algebraic & Geometric Topology 22 (2022) 1217–1253
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Abstract |
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We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities generalizing Ancona’s work on hyperbolic groups. This provides a possibly new metrizable topology on the Morse boundary of such groups. We also prove that the Morse boundary has measure with respect to the harmonic measure unless the group is hyperbolic. |
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Keywords
random walk, Ancona inequalities, hierarchically hyperbolic
group, relatively hyperbolic group
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Mathematical Subject Classification 2010
Primary: 20P05, 20F65, 60J50
Secondary: 20F67, 31C35
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References |
Publication
Received: 21 May 2020
Revised: 12 May 2021
Accepted: 1 July 2021
Published: 25 August 2022
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Authors |
| Matthew Cordes | |
| D-MATH ETH Zürich Zürich Switzerland |
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| Matthieu Dussaule | |
| Institut Denis Poisson Université de Tours Tours France |
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| Ilya Gekhtman | |
| Department of Mathematics Technion-Israel Institute of Technology Haifa Israel |
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